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Easy Geometry: Perpendicular & Angle Bisector Theorems

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Eithar Omer

11/30/2023

Algebra 1

Perpendicular bisectors theorem

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Algebra 1

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Basics

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Overview and History of Algebra

Easy Geometry: Perpendicular & Angle Bisector Theorems

A comprehensive guide to perpendicular and angle bisector theorems in geometry, featuring detailed problem-solving techniques and practical examples. The material covers essential geometric principles with step-by-step solutions for finding unknown values and angles.

  • Step-by-step guide to finding the value of x in geometry problems through algebraic equations and geometric relationships
  • Detailed explanations of perpendicular bisector theorem and its converse, demonstrating how points equidistant from segment endpoints relate to perpendicular bisectors
  • How to solve angle bisector theorem problems with practical applications and real-world examples
  • Clear illustrations of geometric concepts including distance calculations and angle measurements
  • Multiple worked examples showing various problem-solving approaches in geometric constructions
...

11/30/2023

181

Name: Topic: Main Ideas/Questions PERPENDICULAR BISECTOR Theorems 1. Find the value of x. 13x-48=7x724 6x=72 X=12 3. Find RS. Notes/Examples

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Page 2: Angle Bisector Theorems and Advanced Applications

This page delves into angle bisector theorems and their applications in solving geometric problems, including coordinate geometry.

Definition: An angle bisector is a ray that divides an angle into two equal parts.

Highlight: The angle bisector theorem states that any point on an angle bisector is equidistant from the sides of the angle.

Example: Problem 8 shows solving for x using the equation 4x+30=9x-5, yielding x=7.

Quote: "If a point is on the interior of an angle and equidistant from the sides of the angle, then the point is on the angle bisector."

The page includes advanced applications involving coordinate geometry and angle measurements, demonstrating how to verify points lying on perpendicular bisectors using distance formulas.

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Subjects

Algebra 1

Basics

Overview and History of Algebra

 

Algebra 1

•

181

•

Nov 30, 2023

•

2 pages

Easy Geometry: Perpendicular & Angle Bisector Theorems

user profile picture

Eithar Omer

@eitharomer

A comprehensive guide to perpendicular and angle bisector theorems in geometry, featuring detailed problem-solving techniques and practical examples. The material covers essential geometric principles with step-by-step solutions for finding unknown values and angles.

  • Step-by-step guide to finding the value of... Show more

Name: Topic: Main Ideas/Questions PERPENDICULAR BISECTOR Theorems 1. Find the value of x. 13x-48=7x724 6x=72 X=12 3. Find RS. Notes/Examples

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Page 2: Angle Bisector Theorems and Advanced Applications

This page delves into angle bisector theorems and their applications in solving geometric problems, including coordinate geometry.

Definition: An angle bisector is a ray that divides an angle into two equal parts.

Highlight: The angle bisector theorem states that any point on an angle bisector is equidistant from the sides of the angle.

Example: Problem 8 shows solving for x using the equation 4x+30=9x-5, yielding x=7.

Quote: "If a point is on the interior of an angle and equidistant from the sides of the angle, then the point is on the angle bisector."

The page includes advanced applications involving coordinate geometry and angle measurements, demonstrating how to verify points lying on perpendicular bisectors using distance formulas.

Name: Topic: Main Ideas/Questions PERPENDICULAR BISECTOR Theorems 1. Find the value of x. 13x-48=7x724 6x=72 X=12 3. Find RS. Notes/Examples

Sign up to see the contentIt's free!

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Join milions of students

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Page 1: Perpendicular Bisector Theorems and Applications

This page introduces fundamental concepts of perpendicular bisectors and their properties in geometry. The content focuses on practical problem-solving using these theorems.

Definition: A perpendicular bisector is a line that intersects a segment at a 90-degree angle and divides it into two equal parts.

Highlight: The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from the endpoints of the segment it bisects.

Example: Problem 1 demonstrates finding x using the equation 13x-48=7x+24, resulting in x=12 through algebraic manipulation.

Vocabulary: Equidistant means having equal distances from a given point or line.

The page includes multiple practice problems involving finding segment lengths and x-values using algebraic equations derived from geometric relationships.

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Paul T

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

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Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

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Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user